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Study of Hydrological Processes Using a Fractal Geometric Method.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Study of Hydrological Processes Using a Fractal Geometric Method./
Author:	Maskey, Mahesh Lal.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	304 p.
Notes:	Source: Dissertations Abstracts International, Volume: 79-12, Section: B.
Contained By:	Dissertations Abstracts International79-12B.
Subject:	Hydrologic sciences. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10689181
ISBN:	9780355969481

Study of Hydrological Processes Using a Fractal Geometric Method.
Maskey, Mahesh Lal.

Study of Hydrological Processes Using a Fractal Geometric Method. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 304 p.

Source: Dissertations Abstracts International, Volume: 79-12, Section: B.

Thesis (Ph.D.)--University of California, Davis, 2018.

This item must not be sold to any third party vendors.

This research explored how complex natural phenomena can be modeled via a fractal geometric approach, the so-called fractal-multifractal (FM) method. This mathematical and physically-based approach uses fractal functions to transform multifractal measures, related to turbulence, to produce a host of interesting patterns, whose shapes encompass the intricate geometries of diverse geophysical data sets. The evolution of such sets ought to be further studied in order to improve water resource management and to study plausible climate change scenarios. Throughout the research, different variants of the FM notions were used to: (a) encode, (b) simulate, and (c) downscale key signatures of the hydrologic cycle: rainfall, streamflow, and temperature. Regarding encodings, the study investigated whether highly intermittent rainfall sets and mildly intermittent ones of streamflow and temperature, gathered daily over a year, may closely be represented by the FM method. Through the numerical solution of an optimization problem for fractal function parameters and the input multifractal measure, it was found that the notions, carried via iteration of simple maps on the plane, not only captured key statistics of the records, but were also capable of preserving the overall texture present in all data. Further, it was shown that the maximum errors in accumulated records (i.e., their mass functions) did not exceed, for these three attributes (rainfall, streamflow, and temperature), in order, rather small values of 5%, 2% and 1%. These results were deemed excellent and corroborated the goodness of the FM ideas. Concerning simulations, the research tested whether the FM notions were capable of producing plausible simulations of: (i) daily rainfall, (ii) rainfall events (mildly intermittent) lasting a few hours, and (iii) daily streamflow. The answer to this question was affirmative, as it is possible to find, again via an optimization exercise, FM sets that are geometrically indistinguishable from real sets and that closely match key statistics of the records, such as the histogram, and the entropy and autocorrelation functions, which may be preserved not just for a few values as customarily done with other (stochastic) methods, but in their entirety. These remarkable results established the possibility of simulating hydrologic records deterministically and parsimoniously (with less than 8 FM parameters) in order to supplement and enhance stochastic frameworks. Regarding disaggregation, the study demonstrated that the FM approach is capable of generating fine scale (daily) rainfall, streamflow and temperature sets based on coarse scale (weekly, biweekly and monthly) information, which, when compared with real sets, were found to be suitable renderings, both statistically and in their overall texture. These results, and the ones just explained for simulations, ascertained the unconventional and novel notion that determinism may be at the root of complexity. Concentrating on streamflow, the study investigated whether the time evolution of FM parameters may track the dynamics and allow predictions one year ahead. It was found that while evolutions of parameters and geometries vary wildly at the yearly scale, those aggregated at the pentadal and decadal scales exhibited smooth trends, which allow predictions. Such led sometimes, via data-mining classifications of all geometries and the transfer of information via a Markov analysis among scales, to reasonable forecasts for entire years at a time. This relevant result for the planning of water resources was found to hold analyzing at least 65 years of records each at the Sacramento, John Day, Mississippi, and Red River of the North. While usage of FM parameter values revealed that streamflow and temperature sets share similar degrees of complexity, the research established that the rainfall process (at the daily level) is by far the most complex. This was the case as the highly intermittent rain sets at four sites within California: Cherry Valley, Merced, Sacramento and Shasta Dam, showed no obvious trends in parameter evolutions, which were all found to be uncorrelated, and similar, at all sites. In summary, the FM method brings forth a novel approach to study the complexity of hydrological processes, one that, by not requiring statistical assumptions whatsoever, ultimately provides a compact language to describe natural patterns. The encouraging results suggest that the FM notions may be used as a practical tool to aid water resources management and as a relevant scheme for the study of climate change.

ISBN: 9780355969481Subjects--Topical Terms:

3168407
Hydrologic sciences.

Study of Hydrological Processes Using a Fractal Geometric Method.
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245 1 0 $a Study of Hydrological Processes Using a Fractal Geometric Method.
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300 $a 304 p.
500 $a Source: Dissertations Abstracts International, Volume: 79-12, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Puente, Carlos E.;Sivakumar, Bellie.
502 $a Thesis (Ph.D.)--University of California, Davis, 2018.
506 $a This item must not be sold to any third party vendors.
520 $a This research explored how complex natural phenomena can be modeled via a fractal geometric approach, the so-called fractal-multifractal (FM) method. This mathematical and physically-based approach uses fractal functions to transform multifractal measures, related to turbulence, to produce a host of interesting patterns, whose shapes encompass the intricate geometries of diverse geophysical data sets. The evolution of such sets ought to be further studied in order to improve water resource management and to study plausible climate change scenarios. Throughout the research, different variants of the FM notions were used to: (a) encode, (b) simulate, and (c) downscale key signatures of the hydrologic cycle: rainfall, streamflow, and temperature. Regarding encodings, the study investigated whether highly intermittent rainfall sets and mildly intermittent ones of streamflow and temperature, gathered daily over a year, may closely be represented by the FM method. Through the numerical solution of an optimization problem for fractal function parameters and the input multifractal measure, it was found that the notions, carried via iteration of simple maps on the plane, not only captured key statistics of the records, but were also capable of preserving the overall texture present in all data. Further, it was shown that the maximum errors in accumulated records (i.e., their mass functions) did not exceed, for these three attributes (rainfall, streamflow, and temperature), in order, rather small values of 5%, 2% and 1%. These results were deemed excellent and corroborated the goodness of the FM ideas. Concerning simulations, the research tested whether the FM notions were capable of producing plausible simulations of: (i) daily rainfall, (ii) rainfall events (mildly intermittent) lasting a few hours, and (iii) daily streamflow. The answer to this question was affirmative, as it is possible to find, again via an optimization exercise, FM sets that are geometrically indistinguishable from real sets and that closely match key statistics of the records, such as the histogram, and the entropy and autocorrelation functions, which may be preserved not just for a few values as customarily done with other (stochastic) methods, but in their entirety. These remarkable results established the possibility of simulating hydrologic records deterministically and parsimoniously (with less than 8 FM parameters) in order to supplement and enhance stochastic frameworks. Regarding disaggregation, the study demonstrated that the FM approach is capable of generating fine scale (daily) rainfall, streamflow and temperature sets based on coarse scale (weekly, biweekly and monthly) information, which, when compared with real sets, were found to be suitable renderings, both statistically and in their overall texture. These results, and the ones just explained for simulations, ascertained the unconventional and novel notion that determinism may be at the root of complexity. Concentrating on streamflow, the study investigated whether the time evolution of FM parameters may track the dynamics and allow predictions one year ahead. It was found that while evolutions of parameters and geometries vary wildly at the yearly scale, those aggregated at the pentadal and decadal scales exhibited smooth trends, which allow predictions. Such led sometimes, via data-mining classifications of all geometries and the transfer of information via a Markov analysis among scales, to reasonable forecasts for entire years at a time. This relevant result for the planning of water resources was found to hold analyzing at least 65 years of records each at the Sacramento, John Day, Mississippi, and Red River of the North. While usage of FM parameter values revealed that streamflow and temperature sets share similar degrees of complexity, the research established that the rainfall process (at the daily level) is by far the most complex. This was the case as the highly intermittent rain sets at four sites within California: Cherry Valley, Merced, Sacramento and Shasta Dam, showed no obvious trends in parameter evolutions, which were all found to be uncorrelated, and similar, at all sites. In summary, the FM method brings forth a novel approach to study the complexity of hydrological processes, one that, by not requiring statistical assumptions whatsoever, ultimately provides a compact language to describe natural patterns. The encouraging results suggest that the FM notions may be used as a practical tool to aid water resources management and as a relevant scheme for the study of climate change.
590 $a School code: 0029.
650 4 $a Hydrologic sciences. $3 3168407
650 4 $a Civil engineering. $3 860360
650 4 $a Water Resource Management. $3 1669219
690 $a 0388
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710 2 $a University of California, Davis. $b Hydrologic Sciences. $3 1672932
773 0 $t Dissertations Abstracts International $g 79-12B.
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792 $a 2018
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10689181